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A089171
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Numerators of series coefficients of 1/(1 + Cosh[Sqrt[x]]).
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6
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1, -1, 1, -17, 31, -691, 5461, -929569, 3202291, -221930581, 4722116521, -56963745931, 14717667114151, -2093660879252671, 86125672563201181, -129848163681107301953, 868320396104950823611, -209390615747646519456961, 14129659550745551130667441
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Unsigned version is equal to A002425 up to n=11, but differs beyond that point.
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 0..299
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FORMULA
| a(n) = numerator(c(n+1)) where c(n)=(2^(2*n)-1)*B(2*n)/(2*n)!, B(k) denotes the k-th Bernoulli number. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004
Numerators of expansion of cosec(x)-cot(x) = 1/2*x+1/4*x^3/3!+1/2*x^5/5!+17/8*x^7/7!+31/2*x^9/9!+... - Ralf Stephan, Dec 21 2004 (Comment was applied to wrong entry, corrected by Alessandro Musesti (musesti(AT)gmail.com), Nov 02 2007)
E.g.f.: 1/sin(x)-cot(x)=x/G(0); G(k)=4k+2-x^2/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Nov 22 2011
E.g.f.: 1/(1 + cosh(sqrt(x)))=(1+x/(x-2*Q(0))/2; Q(k)=8k+2+x/(1+(2k+1)*(2k+2)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Nov 22 2011
E.g.f.: 1/(1 + cosh(sqrt(x)))=x/(x+Q(0)); Q(k)=x+(x^2)/((4*k+1)*(4*k+2)-(4*k+1)*(4*k+2)/(1+(4*k+3)*(4*k+4)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 22 2011
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MAPLE
| with(numtheory): c := n->(2^(2*n)-1)*bernoulli(2*n)/(2*n)!; seq(numer(c(n)), n=1..20); (C. Ronaldo)
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MATHEMATICA
| Numerator[CoefficientList[Series[1/(1+Cosh[Sqrt[x]]), {x, 0, 24}], x]]
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CROSSREFS
| Cf. A002425, A050970, A002430, A046990.
Sequence in context: A146731 A146667 A146462 * A002425 A046990 A059212
Adjacent sequences: A089168 A089169 A089170 * A089172 A089173 A089174
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KEYWORD
| sign
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Dec 07 2003
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